Realizing high-ranged thermoelectric performance in PbSnS2 crystals

Great progress has been achieved in p-type SnS thermoelectric compound recently, while the stagnation of the n-type counterpart hinders the construction of thermoelectric devices. Herein, n-type sulfide PbSnS2 with isostructural to SnS is obtained through Pb alloying and achieves a maximum ZT of ~1.2 and an average ZT of ~0.75 within 300–773 K, which originates from enhanced power factor and intrinsically ultralow thermal conductivity. Combining the optimized carrier concentration by Cl doping and enlarged Seebeck coefficient through activating multiple conduction bands evolutions with temperature, favorable power factors are maintained. Besides, the electron doping stabilizes the phase of PbSnS2 and the complex-crystal-structure induced strong anharmonicity results in ultralow lattice thermal conductivity. Moreover, a maximum power generation efficiency of ~2.7% can be acquired in a single-leg device. Our study develops a n-type sulfide PbSnS2 with high performance, which is a potential candidate to match the excellent p-type SnS.

are some comments: 1) For the single-leg test, the conversion efficiency is kind of low. Although the high contact resistance was claimed to be the reason for low efficiency, could the authors provide more detailed information on this? 2) Considering that Pb may be regard as one of the main components, the "eco-friendly" may not be a proper word for this material.
3) Since the undoped sample decomposed at 623K, why the authors can still obtain single crystal form of this sample? I think the growth temperature is much higher than 623K, so that one would not get pure phase for undoped sample. 4) Why the electrical conductivity of Cl0.06 sample is lower than that of Cl0.04 sample? More Cl dopant would lead to higher electron concentration, isn't it? 5) For the larger out-of-plane lattice parameter, the authors claimed that it come from interstitials Sni and Pbi. However, it may just because of the substitution of Sn atoms by larger Pb atoms. 6) For the decreasing electron concentration with increasing temperature, the authors claimed that it is caused by the redistribution of electrons in different conduction bands. However,if some acceptors get ionized with increasing temperature, one would also get decreasing electron concentration with increasing temperature. Considering that the cation vacancies are commonly observed in the IV-VI systems, this may be a possible reason for the decreasing electron concentration with increasing temperature.

Reviewer #3 (Remarks to the Author):
The development of low cost, high performance and homojunction structures is particularly important for the large-scale application of thermoelectric devices. Increasing progress on the thermoelectric performance improvement has been made in p-type SnS recently, while the development of n-type SnS seems to be rare. This work developed a novel n-type Snbased sulfide PbSnS2 through alloying Pb at Sn sites and realizing high-ranged thermoelectric performance after growing single crystals and doping Cl in it. Pb alloying was beneficial to suppress Sn vacancies and generate electrons when forming interstitials, while Cl doping enables phase stability and promotes band convergence through optimizing carrier concentration. Combining giant phonon anharmonicity along out-of-plane direction, a favorable average ZT was achieved over a wide temperature range. This manuscript demonstrates for the first time to comprehensively introduce the PbSnS2 as a promising n-type thermoelectric material, which is intriguing. The manuscript should get wide attentions and it will be appreciated by the broader audience. The paper is well organized and carefully written. The novelty and significance are high. Therefore, I believe that this manuscript should be accepted for publication in Nature Communications after some minor revision. Please find below few minor issues-1. The X-ray diffraction of crystal cleavage planes prove the high quality of the synthesized crystals, and the authors should add the X-ray diffraction measurements of corresponding powder to prove that the PbSnS2 single phase is indeed synthesized. Supplementary Fig. 2b, simulated diffraction peaks and Bragg's positions for four models of PbSnS2 have been named repeatedly, the authors should distinguish them.

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3. One key to improve the single-leg power generation efficiency is optimizing the interface structure and conducting layers. So the authors should point out which process was used in the efficiency test.
4. As stated in the supplementary information, the uncertainty of final ZT values is within 20%. Please add error bars to the ZT curve in Fig. 6a. 5. High-ranged thermoelectric performance was realized in PbSnS2 crystals. However, doping is only the first step to optimize the performance of this novel thermoelectric material. The authors would better provide the further potential optimization strategies for readers' reference as few lines outlook in conclusion.
1. The authors mentioned the potential phase decomposition and structural phase transition in the main text but the most commonly used techniques such DSC and TGA were not used for characterization. The authors must perform such measurement to accurately determine the critical temperature points for all samples including the pristine one. Moreover, the reason for the enhanced phase stability of Cl doped samples must be clarified.
Response: Thanks for your valuable comment. We have conducted DSC test to confirm the partial decomposition temperature of the pure sample and structural phase transition temperature of all samples. The results show that the partial decomposition temperature of the pure sample is ~ 623 K, and the structural phase transition temperature of all samples are in the temperature range of 773-823 K. And the results are consistent with the high temperature synchrotron radiation X-ray diffraction (SR-XRD) data. As for the phase stability, we further conducted theoretical calculations on the formation energy of the compound with different compositions, as shown in Supplementary Fig. 7d. The formation energy decreases with the increasing of Cl doping content in PbSnS2, which may be the reason for the enhanced phase stability of the Cl doped samples. Considering the different doping efficiency of Cl element in doped samples, we named the samples based on the room-temperature carrier concentration in our revised manuscript.

Revision:
It is apparent that the total thermal conductivity of undoped PbSnS2 increases abnormally in the medium temperature range, which may be caused by the high thermal conductivity phase PbS as product of partial decomposition ( Supplementary Fig. 7a, c). On the contrary, the lattice thermal conductivity of doped PbSnS2 crystals follows the Umklapp process in the temperature range of 300-773 K, which is due to the fact that Cl doping reduces the formation energy of PbSnS2 and thus enhances the phase stability ( Supplementary Fig. 7b, d).

Supplementary Figure 7.
High temperature SR-XRD data of (a) undoped PbSnS2 and (b) the optimal Cl doped PbSnS2. (c) DSC measurements of Cl doped PbSnS2. The partial decomposition temperature of the undoped sample is ~ 623 K, and the structural phase transition temperature of all samples are in the temperature range of 773-823 K, which are consistent with the SR-XRD data. (d) The comparison of the formation energy between undoped and Cl doped PbSnS2 with different compositions. Phase stability of PbSnS2 was enhanced due to lower formation energy after Cl doping.
2. The authors employed the Debye model for heat capacity estimation in the whole temperature. However, for the temperature region near structural phase transition, such approximation is not valid and the experimental DSC data should be adopted to make correction according to some important references (Phys. Status Solidi RRL 2016, 10, 618;Adv. Mater. 2019, 31, 1806518 Fig. 14 and inset of Fig. 6a). And it is apparent that the results of these three data processing methods are consistent within the 20% error range. 3. Both the band calculations and electrical transport data fitting indicated that a multiple conduction band transport occurs at high temperature. The attained power factor about 4 μW cm -1 K -2 in this work is rather small, even inferior to most of thermoelectric compounds with single band transport feature. So the authors must provide detailed explanation for such contradiction.
Response: Thanks for your valuable comment. In this work, the high performance was obtained along the out-of-plane direction in PbSnS2 crystals due to the ultralow thermal conductivity, however, the power factors are much lower than some thermoelectric compounds with single band transport feature.
The power factor is determined by the Seebeck coefficient and electrical conductivity, which can be further attributed to the carrier concentration, effective mass, and carrier mobility. To solve the aforementioned contradiction, we systematically compare the thermoelectric transport properties of the optimal Cl doped PbSnS2 and n-type PbS. The sample PbS+0.04%PbCl2 (Zhao L.-D., et al. J. Am. Chem. Soc. 133, 20476-20487 (2011)) is selected for comparison because it has single band transport feature and similar carrier concentration (2.75  10 19 cm -3 ) with the optimal Cl doped PbSnS2 (1.7  10 19 cm -3 ).
In the Fig. R1, the Seebeck coefficient of Cl doped PbSnS2 is obviously higher due to the larger effective mass m* (m* = 1.03 me for Cl doped PbSnS2 and m* = 0.40 me for PbS+0.04%PbCl2, me is the electron mass) and multiple conduction bands transport at higher temperatures. The larger effective mass leads to a lower carrier mobility in Cl doped PbSnS2 (μH = 53 cm 2 V -1 s -1 ) along the out-of-plane direction compared with PbS+0.04%PbCl2 (μH = 288 cm 2 V -1 s -1 ), which is an important part of the electrical conductivity.
Therefore, the obtained power factor about 4 μW cm -1 K -2 in this work can be attributed to the low carrier mobility and electrical conductivity. And improving the electric transport performance of the intrinsically low thermal conductive material PbSnS2 through enhancing its carrier mobility is exactly what we will focus on next. 4. It is claimed that the power factor values along the out-of-plane direction is superior to that along the in-plane direction. However, it is controversial to see in Figure 2f that the power factor values along the out-of-plane direction is evidently lower than that along the in-plane direction below 550 K. What is the reason?

Response:
We are sorry for this confusion. In particular, we refer to the power factor along the out-of-plane direction is superior to that along the in-plane direction at higher temperatures. Relevant ambiguous statements have been corrected in revised manuscript.
As can be seen in Supplementary Fig. 6, the power factor along the out-of-plane direction is lower compared with that along the in-plane direction at a relatively low temperature range (300-573 K), which can be attributed to the lower carrier mobility due to interlayer scattering basing on σ = nHeμH. However, the power factor along the out-of-plane direction is superior at relatively high temperature range due to the gradual increase of interlayer charge density (Fig. 3), which makes PbSnS2 also possess the characteristics of 3D charge and 2D phonon transports like n-type SnSe and SnS (Chang C., et al. Science 360, 778-783 (2018);Hu X., et al. Scripta Mater. 170, 99-105 (2019)).
Revision: Compared with the in-plane direction, our results show that higher thermoelectric performance is achieved along the out-of-plane direction due to the ultralow thermal conductivity from strong interlayer phonon scattering and superior power factor at higher temperatures (>600K) due to increased interlayer charge density, which is similar to the anisotropy of n-type SnSe.
5. If the structural phase transition indeed occurs above 773 K, the calculation of average ZT within 300-823 K is meaningless since structural phase transition leads to failure of thermoelectric device and thus such estimation is not practical.
6. The measured device efficiency of 0.8% is too low to adequately demonstrate the practical potential for this compound even though the authors refer to contact resistance. The authors must make some good devices and measure their performance if they really want to prove the practical potential of these crystals in the high profile journal like nature communications.
Response: Thanks for the valuable comment. The fabrication process and contacting materials of the device have great impact on the measurement of the device efficiency. Optimizing the fabrication process and contacting materials of the device can further optimize the conversion efficiency. On this basis, we have fabricated a new device using electroplated nickel as the barrier layer and gold foil as metallization contacting layer. The maximum single-leg power generation efficiency measured in PbSnS2 is ~ 2.7% with a maximum output power of ~ 18 mW at a temperature difference of ~ 377 K (Fig. 6c,d), which is comparable to the maximum conversion efficiency of ~ 3.0% achieved in p-type SnS crystals (He W., et al. Science 365, 1418-1424(2019). However, we must say that the current device performance is still far away from expected, but this optimization by electroplating the barrier layer has to some extent reflecting the application potential for PbSnS2 crystals, especially considering the great difficulty of reducing the contact resistance in the out-of-plane direction of the crystals.

Fig. 6c
Output power P, the inset shows the mini-PEM test. d Power generation efficiency η for single-leg device based on the optimal Cl doped PbSnS2 crystal. Comparison of single-leg power generation efficiency between the optimal Cl doped PbSnS2 crystal in this work and p-type SnS crystal.
7. In Fig. 4 and Fig. 5, it is apparent that the high symmetry points used to describe band path in the electronic and phonon structures are not consistent. The authors should give their specific reason for this.

Response:
We are sorry for this confusion. In the electronic band structure calculation of Fig. 4, we mainly focus on the relative positions of CBM1, CBM2 and CBM3. The lattice thermal conductivity is mainly originated from acoustic phonon mode, thus the phonon spectrum presented along a, b and c directions in Fig. 5. Our different focus leads to the inconsistency of high symmetry points in the band structure and phonon spectrum calculations.

Reviewer #2 (Remarks to the Author):
Comments: High TE performance was found in PbSnS2 crystals doped by Cl on S sites. Both increased electron concentration and the convergence of conduction bands were found to be responsible to the enhanced electrical transport properties. It is an interesting result. Here are some comments: Response: Thanks for your affirmation of our work. Your insightful comments will help to improve our work.
1. For the single-leg test, the conversion efficiency is kind of low. Although the high contact resistance was claimed to be the reason for low efficiency, could the authors provide more detailed information on this?
Response: Thanks for your good suggestions. As for using crystal samples to fabricate thermoelectric devices, the contacting resistance is rather high due to the special and oriented arrangement of atoms, especially for the out-of-plane direction. We further optimized the fabrication process and contacting materials of the device and achieved better results. The maximum single-leg power generation efficiency after optimization can reach ~2.7%, where nickel was electroplated onto the cleavage surface as a barrier layer and gold foil was used as contact material to lower contact resistance.
Revision: Single-leg power generation efficiency test. The single-leg device was fabricated using the optimal Cl doped PbSnS2 crystal with the geometrical dimension of ~ 2 mm (length) × 3 mm (width) × 6 mm (height), where nickel was electroplated onto the cleavage surface as a barrier layer and gold foil was used as contact material. Mini-PEM Ulvac-Riko (Japan) was adopted for the direct data of output power and conversion efficiency while the cold-side temperature (Tc) was maintained at 295 K and the hot-side temperature (Th) was varied from 397 K to 672 K.
incorporate into the PbSnS2 lattice will cause many defects and impurities containing Cl, thus reducing the carrier mobility of the material and deteriorating the electric transport performance. The phenomenon that the carrier concentration decreases when the dopant is excessive slightly also appears in Na-doped SnS crystals (Wu H., et al. Adv. Energy. Mater. 8, 1800087 (2018)). Moreover, considering these reasons, we named the samples based on the room-temperature carrier concentration, which was also conducted in Br and Cl doped SnSe crystals (Chang C., et al. Science 360, 778-783 (2018);Su L., et al. Science 375, 1385-1389(2022).

5.
For the larger out-of-plane lattice parameter, the authors claimed that it come from interstitials Sni and Pbi. However, it may just because of the substitution of Sn atoms by larger Pb atoms.
Response: Sorry for confusing you. According to existing studies in the literature, Pb substitution enlarges the interlayer distance due to its larger ionic radius, which makes the formation of Sn and Pb interstitials easier because of the reduction of the formation enthalpies of Sn and Pb interstitials (Xiao Z., et al. Appl. Phys. Lett. 106, 152103 (2015)). Therefore, the logic is that the larger out-of-plane lattice parameter in PbSnS2 compared with SnS comes from the substitution of larger Pb atoms, which might lead to interstitials Sni and Pbi.
Revision: Also, the lattice parameter of PbSnS2 along the out-of-plane direction increases by ~ 0.24 Å compared with SnS because of the enlarged interlayer distance by larger Pb 2+ ions substitution, which is conducive to the formation of interstitials Sni and Pbi.
6. For the decreasing electron concentration with increasing temperature, the authors claimed that it is caused by the redistribution of electrons in different conduction bands. However, if some acceptors get ionized with increasing temperature, one would also get decreasing electron concentration with increasing temperature. Considering that the cation vacancies are commonly observed in the IV-VI systems, this may be a possible reason for the decreasing electron concentration with increasing temperature.
Response: Thanks for your valuable comment. This may be another reason why the carrier concentration decreases with temperature. And we included the possibility in revised manuscript.
Revision: However, our results show that the carrier concentration has an obvious decreasing trend with temperature rising, indicating that the cation vacancies may be excited or electrons may be redistributed among the multiple conduction bands at higher temperatures.